Tricomi Problem for Second Kind Parabolic Hyperbolic Type Equation

Abstract

In the work Tricomi problem was investigated for a parabolic-hyperbolic type equation in a mixed domain. If the parabolic degeneration line is a characteristic of a hyperbolic equation, then Tricomi problem for considered equation will not be uniquely solvable. Therefore, another formulation of Tricomi problem was proposed which the gluing condition is given as in [1, 2]. To study Tricomi problem in the hyperbolic part of the domain, $$R_{00}^{\lambda}$$ class of the regular solutions of the view changed Cauchy problem for the equation of the hyperbolic part are introduced. An explicit form of the solution is found for the Cauchy problem from this class. The solution of the Tricomi problem in the hyperbolic part of the domain is found as a regular solution from the class $$R_{00}^{\lambda}$$ of the view changed Cauchy problem, and in the parabolic part of the domain as the solution of the first boundary value problem. For proving the existence of the solution of the problem, the theory of second kind Volterra integral equations is used.